When planning out my math for the year, representing whole numbers to one million (for Grade 6) and one billion (for Grade 7) is the second most important unit of the year. The most important unit is the growth mindset one that you can read about here and here.
This unit sets the standard for what the students need to know. If they don’t know how to read and represent numbers in different ways then they may have some difficulty with every other unit we do!
Here are my favourite ways to help my students really understand large numbers. If you love these ideas, then you should check out the Representing Whole Numbers to 1 Million and 1 Billion Units. These units include full lesson plans, math talks, open-ended problems & activities, exit tickets, and a unit test. Pretty much everything you need!
1. How much is a million?
A million is a pretty big number for students but just how big is it? Read “How Much is a Million?” by David M. Schwartz and have students jot down what surprised them as you read.
Then, do a problem-solving activity where they need to really see just how big a million is. I love this water problem as students need to do some investigation (how much water do people drink in a day) and some metric conversion (converting cups to mL to L).
2. Representing whole numbers with base ten blocks
Using base ten blocks will give your students a concrete representation of numbers. It is necessary for students to make that leap from concrete to pictorial to abstract representations.
Tell your students to select a certain number of blocks. For example, 22. What numbers can they represent using 22 base ten blocks? Keeping it open-ended like this allows students to pick the blocks that they are comfortable using.
Then have students put that number in a place value chart.
Using the same number of blocks, what other numbers can they represent?
3. What's my number?
“What’s My Number?” is a great math talk you can use with your students to help them rename numbers. For example, 594 000 can be renamed as 5 940 hundreds, 594 thousands, and 59.4 ten thousands.
Show your students a slide that looks like this:
Make sure students can justify their answers.
4. Expressing numbers in expanded notation
Random number generators can be your friend. Have your students use one to generate a number that is close to 1 million. They can then write the number in expanded notation and in words.
Then, create a large open-number line on your board and have students place their number on the appropriate spot.
Knowing how to represent whole numbers with base ten blocks, in place value charts, on number lines, and in expanded notation will really help them to make the connection to decimal numbers. Place value is the key!
You can get more information about this unit by clicking here.
If you are looking for some long range plans to guide your math and language planning then you definitely need to download these free ones!
I’m Lauren, from “From Math to Music” – your go-to person for all things Math and Classroom Community.
Being a middle-school teacher and a mom of 3, I know how hard it is for busy teachers to create resources that allow for deep thinking and build classroom community. That's why I love sharing tips and tricks that you can you use in your middle school classroom right this minute.
